谢绪恺、聂义勇判据的提出 比国外学者的同类发现要早得多。由于历史原因,这判据过去未曾宣扬。81年本刊上的简要介绍 曾引起了我国广大读者的重视和兴趣。现在,应读者要求,再作一次较详细的介绍。谢聂判据,简单地说,就是:(A)给多项式式 a_0x~n+a_1x~(n-1)+…+a_n 或 a_0+a_1+…+a_nx~n(a_i>0,i=0,1,2,…n)定义一判定系数α_i=a_i-|a|+2/a_ia_i+1,(B)多项式所表征的系统的稳定性由这判定系数α_i 判定,稳定的必要条件是α_(?)<1,充分条件是α_i<0.4655。 Xie Xu Kai, Nie Yi-yong criteria proposed earlier than similar discoveries by foreign scholars much earlier. For historical reasons, this criterion has not been advertised in the past. 81 years The brief introduction in this magazine has aroused the attention and interest of our readers. Now, at the reader’s request, make a more detailed introduction. The Xie Xie criterion is simply: (A) Give a polynomial a_0x ~ n + a_1x ~ (n-1) + ... + a_n or a_0 + a_1 + ... + a_nx ~ n (a_i> 0, i = 0, 1, 2, ... n) define a decision coefficient α_i = a_i- | a | + 2 / a_ia_i + 1, (B) The stability of the system represented by the polynomial is judged by this decision coefficient α_i. The necessary condition for stability is α_ ?) <1, the sufficient condition is α_i <0.4655.